S= 5+5²+5³+...+5²⁰²⁰+5²⁰²¹

 5S=5²+5³+5⁴+...+5²⁰²¹+5²⁰²²

 5S - S=4S=5²⁰²²-5

  Ta có: 4S+5=5²⁰²²

             =4S -5 +5 =5²⁰²²

              => 4S=5²⁰²²

\(\left(5^{2021}-5^{2020}\right):5^{2020}=5^{2021}:5^{2020}-5^{2020}:5^{2020}=5-1=4\)

làm ơn đi, mình đang cần gắp.

\(\dfrac{5^{2021}}{5^{2020}}\cdot5^2=5\cdot5^2=5^3\)

5²⁰²¹:5²⁰²⁰. 5²

= 5¹.5²

=5³

5^2021 : 5^2020 x 5^2

=  5^1 x 5^2

= 5^3

giúp ik

Bài 1 :

\(M=\dfrac{30-2^{20}}{2^{18}}=\dfrac{2.15-2^{20}}{2^{18}}=\dfrac{15}{2^{17}}-2^2=\dfrac{15}{2^{17}}-4< 0\left(\dfrac{15}{2^{17}}< 1\right)\)

\(N=\dfrac{3^5}{1^{2021}+2^3}=\dfrac{3^5}{9}=\dfrac{3^5}{3^2}=3^3=27\)

\(\Rightarrow M< N\)

Bài 3 :

a) \(t^2+5t-8\) khi \(t=2\)

\(=5^2+2.5-8\)

\(=25+10-8\)

\(=27\)

b) \(\left(a+b\right)^2-\left(b-a\right)^3+2021\left(1\right)\)

\(\left\{{}\begin{matrix}a=5\\b=a+1=6\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}a+b=11\\b-a=1\end{matrix}\right.\)

\(\left(1\right)=11^2-1^3+2021=121-1+2021=2141\)

c) \(x^3-3x^2y+3xy^2-y^3=\left(x-y\right)^3\left(1\right)\)

\(\left\{{}\begin{matrix}x=3\\y=2\end{matrix}\right.\) \(\Rightarrow x-y=1\)

\(\left(1\right)=1^3=1\)

Bài 2 :

a) \(...=2^3\left(19-14\right)+1=8.5+1=41\)

b) \(...=100-\left[60:\left(5^2-15\right)\right]=100-\left[60:10\right]=100-6=94\)

c) \(...=160:\left[17+\left(9.5-\left(14+2^3\right)\right)\right]=160:\left[17+\left(45-22\right)\right]=160:\left[17+23\right]=160:40=4\)

d) \(...=798+100\left[16-2\left(25-22\right)\right]=798+100\left[16-2.3\right]=798+100.10=798+1000=1798\)

\(A=5+5^2+5^3+...+5^{2021}\)

\(\Rightarrow A=\left(5^1+5^2\right)+5^2\left(5^1+5^2\right)...+5^{2018}\left(5^1+5^2\right)+5^{2021}\)

\(\Rightarrow A=30+5^2.30...+5^{2018}.30+5^{2021}\)

\(\Rightarrow A:30=1+5^2+...+5^{2018}+\dfrac{5^{2021}}{30}\)

\(\Rightarrow A:30=1+5^2+...+5^{2018}+\dfrac{5^{2020}}{6}\)

số dư là bao nhieu ạ ?

đề bài tìm số dư ạ 

Số dư là \(\dfrac{5^{2020}}{6}\)

a: =5-78*32

=5-2496

=-2491

b: \(=6\left(9-6\right)=6\cdot3=18\)

c: \(=46\cdot\dfrac{\left(123-42\right)}{81}=46\)

d: \(=181+3-84+8\cdot25\)

=100+200

=300

e: \(=64\cdot35+140\cdot84-1=2240-1+11760\)

=14000-1

=13999

f: \(=3^3+25\cdot8-1=26+200=226\)

g: \(=3+2^4+1=16+4=20\)

h: \(=36:4\cdot3+2\cdot25-1=27+50-1=27+49=76\)